I don't really think Newcomb's problem or any of its variations belong in here. Newcomb's problem is not a decision theory problem, the real difficulty is translating the underspecified English into a payoff matrix.

The ambiguity comes from the the combination of the two claims, (a) Omega being a perfect predictor and (b) the subject being allowed to choose after Omega has made its prediction. Either these two are inconsistent, or they necessitate further unstated assumptions such as backwards causality.

First, let us assume (a) but not (b), which can be formulated as follows: Omega, a computer engineer, can read your code and test run it as many times as he would like in advance. You must submit (simple, unobfuscated) code which either chooses to one- or two-box. The contents of the boxes will depend on Omega's prediction of your code's choice. Do you submit one- or two-boxing code?

Second, let us assume (b) but not (a), which can be formulated as follows: Omega has subjected you to the Newcomb's setup, but because of a bug in its code, its prediction is based on someone else's choice than yours, which has no correlation with your choice whatsoever. Do you one- or two-box?

Both of these formulations translate straightforwardly into payoff matrices and any sort of sensible decision theory you throw at them give the correct solution. The paradox disappears when the ambiguity between the two above possibilities are removed. As far as I can see, all disagreement between one-boxers and two-boxers are simply a matter of one-boxers choosing the first and two-boxers choosing the second interpretation. If so, Newcomb's paradox is not as much interesting as poorly specified. The supposed superiority of TDT over CDT either relies on the paradox not reducing to either of the above or by fiat forcing CDT to work with the wrong payoff matrices.

I would be interested to see an unambiguous and nontrivial formulation of the paradox.

Some quick and messy addenda:

- Allowing Omega to do its prediction by time travel directly contradicts
*box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes*. Also, this obviously make one-boxing the correct choice. - Allowing Omega to accurately simulate the subject reduces to problem to
*submit code for Omega to evaluate*; this is not exactly paradoxical, but then*the player is called upon to choose which boxes to take*actually means*the code then runs and returns its expected value*, which clearly reduces to one-boxing. - Making Omega an imperfect predictor, with an accuracy of p<1.0 simply creates a superposition of the first and second case above, which still allows for straightforward analysis.
- Allowing unpredictable, probabilistic strategies violates the supposed predictive power of Omega, but again cleanly reduces to payoff matrices.
- Finally, the number of variations such as the
*psychopath button*are completely transparent, once you decide between*choice is magical and free will and stuff*which leads to pressing the button, and*the supposed choice is deterministic and there is no choice to make, but code which does not press the button is clearly the most healthy*.

*9 points [-]